Clinical consequences of relative biological effectiveness variations in proton radiotherapy of the prostate, brain and liver

Proton relative biological effectiveness (RBE) is known to depend on the (alpha/beta)(x) of irradiated tissues, with evidence of similar to 60% variation over (alpha/beta)(x) values from 1-10 Gy. The range of (alpha/beta)(x) values reported for prostate tumors (1.2-5.0 Gy), brain tumors (10-15 Gy) and liver tumors (13-17 Gy) imply that the proton RBE for these tissues could vary significantly compared to the commonly used generic value of 1.1. Our aim is to evaluate the impact of this uncertainty on the proton dose in Gy(RBE) absorbed in normal and tumor tissues. This evaluation was performed for standard and hypofractionated regimens. RBE-weighted total dose (RWTD) distributions for 15 patients (five prostate tumors, five brain tumors and five liver tumors) were calculated using an in-house developed RBE model as a function of dose, dose-averaged linear energy transfer (LETd) and (alpha/beta)(x). Variations of the dose-volume histograms (DVHs) for the gross tumor volume (GTV) and the organs at risk due to changes of (alpha/beta)(x) and fractionation regimen were calculated and the RWTD received by 10% and 90% of the organ volume reported. The goodness of the plan, bearing the uncertainties, was then evaluated compared to the delivered plan, which considers a constant RBE of 1.1. For standard fractionated regimens, the prostate tumors, liver tumors and all critical structures in the brain showed typically larger RBE values than 1.1. However, in hypofractionated regimens lower values of RBE than 1.1 were observed in most cases. Based on DVH analysis we found that the RBE variations were clinically significant in particular for the prostate GTV and the critical structures in the brain. Despite the uncertainties in the biological input parameters when estimating RBE values, the results show that the use of a variable RBE with dose, LETd and (alpha/beta)(x) could help to further optimize the target dose in proton treatment planning. Most importantly, this study shows that the consideration of RBE variations could influence the comparison of proton and photon treatments in clinical trials, in particular in the case of the prostate

The influence of molecular reach and diffusivity on the efficacy of membrane-confined reactions

Signaling by surface receptors often relies on tethered reactions whereby an enzyme bound to the cytoplasmic tail of a receptor catalyzes reactions on substrates within reach. The overall length and stiffness of the receptor tail, the enzyme, and the substrate determine a biophysical parameter termed the molecular reach of the reaction. This parameter determines the probability that the receptor-tethered enzyme will contact the substrate in the volume proximal to the membrane when separated by different distances within the membrane plane. In this work, we develop particle-based stochastic reaction-diffusion models to study the interplay between molecular reach and diffusion. We find that increasing the molecular reach can increase reaction efficacy for slowly diffusing receptors, whereas for rapidly diffusing receptors, increasing molecular reach reduces reaction efficacy. In contrast, if reactions are forced to take place within the two-dimensional plasma membrane instead of the three-dimensional volume proximal to it or if molecules diffuse in three dimensions, increasing molecular reach increases reaction efficacy for all diffusivities. We show results in the context of immune checkpoint receptors (PD-1 dephosphorylating CD28), a standard opposing kinase-phosphatase reaction, and a minimal two-particle model. The work highlights the importance of the three-dimensional nature of many two-dimensional membrane-confined interactions, illustrating a role for molecular reach in control-ling biochemical reactions.Published versio

Stirring Times in Austria, 1898

Article, 27 pagesMark Twain spent two years (1897-1899) traveling in Central Europe, staying mostly in Vienna. While there, he reported on the famous sittings of the Austrian House in 1897 during which the conservative government sought to push through the renewal of the Ausgleich [Compromise] agreement against the will of the German Liberals (Twain calls them "the Left" or "the Opposition"). The government at the time was headed by Count Badeni (a Polish aristocrat whose full name was Kazimierz Felix), known as a "strong man" for his overbearing governance of Galicia. His appointment resulted in the slow collapse of German control over the monarchy. The reason for the 1897 legislative crisis was that Badeni had issued a language ordinance that gave Czech equal status with German even within the "inner service" (meaning between government departments). The German liberal opposition was so incensed that it vowed to obstruct the Ausgleich renewal until, in Twain?s words, "the obnoxious Czech-language measure should be shelved." In the wake of the often violent protests, both within the House and in Prague, Vienna, Graz, and elsewhere in the monarchy, Emperor Franz Joseph dismissed Badeni. In the absence of a majority within the House, however, legislative action came to be undertaken increasingly by imperial emergency provisions which the parliament was not in session. This in turn further sapped the government of its remaining legitimacy. Twain outlines all these events with characteristic wit in this piece

On the Classification of Vertex-Transitive Structures

We consider the classification problem for several classes of countable structures which are “vertex-transitive”, meaning that the automorphism group acts transitively on the elements. (This is sometimes called homogeneous.) We show that the classification of countable vertex-transitive digraphs and partial orders are Borel complete. We identify the complexity of the classification of countable vertex-transitive linear orders. Finally we show that the classification of vertex-transitive countable tournaments is properly above E0 in complexity